I run 64 bit linux Pale Moon 25.3.0 in 64 bit linux Mint 17 "Qiana" (and 64 bit linux Mint 17.1 "Rebecca" in my second desktop tower computer) without any problems. Keep in mind I'm not a power user in either Linux or Windows. I'm a non-technical computer average user so if anyone is going to have problems with linux Pale Moon, it'll be me and like I just said, "no problems".

I run the 64 bit on my Manjaro Linux box (plus in a couple 64 bit VM's, and occasionally the 32 bit in a VM as well), and my wife uses the 64 bit on her Linux Mint 17.1 box. Our OS's are different, with Manjaro being a rolling release distro, whereas Linux Mint is a fixed release distro (here is a good article on the differences, if you're interested). Our browsing habits are also very different: I generally do a lot of searching and research online, going to many different and new sites all the time every day, whereas my wife generally sticks to just a handful of sites she normally visits. All that to say neither one of us has ever encountered any kind of an issue with Pale Moon on Linux.

FYI, if you use the installer for Linux, it will automatically download and extract the correct version based on your OS (32 bit or 64 bit).